Quiz — درس الإحتمالات السنة الثانية آداب2.doc

Question 1 sur 10 20:00

[{"id":47248,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé équilibré a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":47249,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir au hasard une fille dans cette classe ?","option_a":"0.3","option_b":"0.4","option_c":"0.5","option_d":"0.6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 12 filles sur 30 élèves. La probabilité est donc 12\/30 = 0.4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.3\", \"b\": \"0.4\", \"c\": \"0.5\", \"d\": \"0.6\"}}","_debug_options_count":4},{"id":47250,"question":"Deux événements A et B sont incompatibles si P(A ∩ B) = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux événements sont incompatibles si leur intersection est vide, c'est-à-dire P(A ∩ B) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47251,"question":"Quelle est la probabilité d'obtenir deux fois pile en lançant deux fois une pièce équilibrée ?","option_a":"1\/4","option_b":"1\/2","option_c":"3\/4","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d'obtenir pile une fois est 1\/2. Pour deux lancers indépendants, c'est (1\/2) × (1\/2) = 1\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/4\", \"b\": \"1\/2\", \"c\": \"3\/4\", \"d\": \"1\"}}","_debug_options_count":4},{"id":47252,"question":"Si P(A) = 0.7 et P(B) = 0.5, quelle est la probabilité maximale de P(A ∩ B) ?","option_a":"0.5","option_b":"0.7","option_c":"1.2","option_d":"0.35","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité maximale de P(A ∩ B) est le minimum entre P(A) et P(B), soit 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.5\", \"b\": \"0.7\", \"c\": \"1.2\", \"d\": \"0.35\"}}","_debug_options_count":4},{"id":47253,"question":"Un sac contient 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer une boule bleue ?","option_a":"3\/5","option_b":"3\/8","option_c":"5\/8","option_d":"8\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 3 boules bleues sur un total de 8 boules. La probabilité est donc 3\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\/5\", \"b\": \"3\/8\", \"c\": \"5\/8\", \"d\": \"8\/3\"}}","_debug_options_count":4},{"id":47254,"question":"Si deux événements A et B sont indépendants, alors P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux événements sont indépendants si la réalisation de l'un n'influence pas l'autre, donc P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47255,"question":"Dans une urne avec 4 boules vertes et 6 boules jaunes, quelle est la probabilité de tirer une boule verte ou une boule jaune ?","option_a":"0.4","option_b":"0.6","option_c":"1","option_d":"0.24","option_e":"","option_f":"","bonne_reponse":"c","explication":"Toutes les boules sont soit vertes soit jaunes, donc la probabilité est 1 (100%).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0.4\", \"b\": \"0.6\", \"c\": \"1\", \"d\": \"0.24\"}}","_debug_options_count":4},{"id":47256,"question":"Quelle est l'espérance mathématique d'une variable aléatoire X qui prend les valeurs 1, 2 et 3 avec les probabilités respectives 0.2, 0.5 et 0.3 ?","option_a":"2.1","option_b":"2.2","option_c":"2.3","option_d":"2.4","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance se calcule par E(X) = 1×0.2 + 2×0.5 + 3×0.3 = 0.2 + 1.0 + 0.9 = 2.1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2.1\", \"b\": \"2.2\", \"c\": \"2.3\", \"d\": \"2.4\"}}","_debug_options_count":4},{"id":47257,"question":"La variance d'une variable aléatoire mesure la dispersion des valeurs autour de l'espérance.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance quantifie la dispersion des valeurs d'une variable aléatoire autour de sa moyenne (espérance).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]